Place Value Challenge: Finding a Number with Specific Digits (1,8,4,7,2)

The problem requires us to construct a number with specific digits assigned to certain decimal places. Let's go through this step-by-step:

• Step 1: Identify the given digits for each specified place value in the number:
  - Hundreds of thousands digit should be $1$.
  - Tens of thousands digit should be $8$.
  - Thousands digit should be $4$.
  - Tens digit should be $7$.
  - Units digit should be $2$.
• Step 2: Determine positions that are unspecified:
  - The hundreds place is not specified, so it defaults to zero.
• Step 3: Construct the number using the given digits:
  - Place $1$ in the hundreds of thousands place.
  - Place $8$ in the tens of thousands place.
  - Place $4$ in the thousands place.
  - Place $0$ in the hundreds place.
  - Place $7$ in the tens place.
  - Place $2$ in the units place.
• Step 4: Write out the complete number:

The number we form is $184,072$.

Comparing this number with the answer choices:
Choice 4 matches the number we constructed: $184,072$.

Therefore, the correct answer is $184,072$.